Chapter 1.8, Problem 45P

To determine

Show that if the conditional probabilities exist, then

$P\left(A_1\cap A_2\cap \mathrm{...}\cap A_n\right)=P\left(A_1\right)P\left(A_2|A_1\right)P\left(A_3|A_1\cap A_2\right)\mathrm{...}P\left(A_n|A_1\cap A_2\cap \mathrm{...}\cap A_{n-1}\right)$.